For a closed cylinder with radius r ⁢ cm and height h ⁢ cm, find the dimensions giving the minimum surface area, given that the volume is 36 cm3.

The radius is 1.79 cm and height is 3.58 cm.

Step-by-step explanation:

The surface area of the closed cylinder is given by,

And volume is given by,

Where, R is radius and h is height of cylinder.

Volume is given to be  36 cm3.

Inserting this value of h in Surface area equation, we get,

Now differentiating wrt x to find minimum, inserting , we get,

Thus, h = 3.58 cm from above equation.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!